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Parameterizations for cloud single-scattering properties and the scaling of optical thickness in a partial cloudiness condition have been developed for use in atmospheric models. Cloud optical properties are parameterized for four broad bands in the solar (or shortwave) spectrum; one in the ultraviolet and visible region and three in the infrared region. The extinction coefficient, single-scattering albedo, and asymmetry factor are parameterized separately for ice and water clouds. Based on high spectral-resolution calculations, the effective single-scattering coalbedo of a broad band is determined such that errors in the fluxes at the top of the atmosphere and at the surface are minimized. This parameterization introduces errors of a few percent in the absorption of shortwave radiation in the atmosphere and at the surface. Scaling of the optical thickness is based on the maximum-random cloud-overlapping approximation. The atmosphere is divided into three height groups separated approximately by the 400- and 700-mb levels. Clouds are assumed maximally overlapped within each height group and randomly overlapped among different groups. The scaling is applied only to the maximally overlapped cloud layers in individual height groups. The scaling as a function of the optical thickness, cloud amount, and the solar zenith angle is derived from detailed calculations and empirically adjusted to minimize errors in the fluxes at the top of the atmosphere and at the surface. Different scaling is used for direct and diffuse radiation. Except for a large solar zenith angle, the error in fluxes introduced by the scaling is only a few percent. In terms of absolute error, it is within a few watts per square meter.
Chou et al. (Sun,) studied this question.